Teorema de Furry

O Teorema de Furry é um resultado em Teoria Quântica de Campos, em particular Eletrodinâmica Quântica, sobre amplitudes e diagramas, que afirma que diagramas contendo um número ímpar de vértices da teoria necessariamente se anulam. Uma outra maneira de enunciar o teorema é que qualquer amplitude obtida a partir de diagramas de Feynman com apenas um número ímpar de linhas de fótons externos é sempre nula.[1]. Isso se deve à simetria C e também à invariância por Lorentz. Um corolário importante é que não é possível gerar ou destruir fótons que não sejam virtuais a partir do vácuo da EDQ[2].

O teorema foi obtido primeiramente por Wendell H. Furry em 1937[3], nos princípios do que viria a se tornar a Eletrodinâmica Quântica.


Diagrama de Feynman da EDQ com três linhas bosônicas.
Diagrama de Feynman com três linhas externas de fótons. Este diagrama é anulado devido ao teorema de Furry, assim como qualquer diagrama que o contenha internamente.

Heurística do Teorema

O teorema advém diretamente da natureza do vértice da EDQ, que inclui um termo do operador corrente eletromagnética. Uma amplitude obtida a partir de um diagrama com um vértice contém um termo do tipo[2]:318

,

e como sabemos que uma corrente inverte de sinal ao aplicarmos uma transformação C, podemos sanduichar os operadores , na expressão acima, observando que como C é uma simetria da EDQ, o vácuo é invariante por essa transformação

,

e obter

.

Apesar do raciocínio aqui se aplicar apenas a amplitudes com um vértice, ele é generalizável para amplitudes e diagramas contendo uma quantidade ímpar de vértices, inclusive para teoria de perturbação em qualquer ordem.

Uma outra maneira de obter o resultado é fazendo uso da simetria de Lorentz da EDQ e da invariância do vácuo da teoria , notando que não pode existir um quadrivetor preferencial.

É importante notar que o teorema faz uso fundamental das simetrias da EDQ, então ele pode não ser aplicado a outras TQC necessariamente.

Veja também


Referências

  1. ↑ Weinberg, Steven (1995). The Quantum Theory of Fields. [S.l.]: Cambridge University Press. ISBN 978-0-521-55001-7 
  2. ↑ a b Peskin, Michael E. (1995). An Introduction To Quantum Field Theory (em inglês). [S.l.]: CRC Press. ISBN 978-0-429-97210-2 
  3. ↑ Furry, W. H. (15 de janeiro de 1937). «A Symmetry Theorem in the Positron Theory». Physical Review (em inglês). 51 (2): 125–129. ISSN 0031-899X. doi:10.1103/PhysRev.51.125 

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